The term \((\Omega _i^{k})^{(1)}\)  is the usual single relaxation time Bhatnagar–Gross–Krook collisional operator [1]}
\( (\Omega _i^{k})^{(1)}=\frac{f_{i,eq}^k(\mathbf {u},\mathbf {x},t)-f_i^k(\mathbf {x},t)}{\tau },\) 
